Related papers: Asymptotic confidence bands for centered purely ra…
The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
We consider the infinite-horizon average-reward restless bandit problem. We propose a novel \emph{two-set policy} that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
We investigate the asymptotic behavior, in the long time limit, of the random homology associated to realizations of stochastic diffusion processes on a compact Riemannian manifold. In particular a rigidity result is established: if the…
With the aid of simple analytical computations for the Ehrenfest model, we clarify some basic features of macroscopic irreversibility. The stochastic character of the model allows us to give a non-ambiguous interpretation of the general…
We present methodology for constructing pointwise confidence intervals for the cumulative distribution function and the quantiles of mixing distributions on the unit interval from binomial mixture distribution samples. No assumptions are…
We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…
Random forests have become an important tool for improving accuracy in regression and classification problems since their inception by Leo Breiman in 2001. In this paper, we revisit a historically important random forest model originally…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…
Stochastic linear bandits are a natural and simple generalisation of finite-armed bandits with numerous practical applications. Current approaches focus on generalising existing techniques for finite-armed bandits, notably the optimism…
We establish the consistency of an algorithm of Mondrian Forests, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm, that considers a fixed lifetime parameter.…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
Adaptively collected data has become ubiquitous within modern practice. However, even seemingly benign adaptive sampling schemes can introduce severe biases, rendering traditional statistical inference tools inapplicable. This can be…
Let $T\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to…
We investigate the problem of finding confidence sets for split points in decision trees (CART). Our main results establish the asymptotic distribution of the least squares estimators and some associated residual sum of squares statistics…
We consider the infinite-horizon, average-reward restless bandit problem in discrete time. We propose a new class of policies that are designed to drive a progressively larger subset of arms toward the optimal distribution. We show that our…